Chapter 16 Page 1 of 6

WebQuizzing – Ch. 16

Book ISBN-10 0538477490

Book ISBN-13 9780538477499

Author: Gerald Keller

Title: Statistics for Management and Economics

Ed: 9e

# Questions Submitted: 20 Multiple Choice

  1. Given the least squares regression line = 5 –2x:
  1. the relationship between x and y is positive.
  2. the relationship between x and y is negative.
  3. as x decreases, so does y.
  4. None of these choices.

Analysis:

A. Incorrect. The relationship between x and y is negative.

B. Correct. The relationship between x and y is negative.

C. Incorrect. The relationship between x and y is negative.

D. Incorrect. The relationship between x and y is negative.

ANSWER: B Ref: Section 16.1-16.2

  1. In the simple linear regression model, the slope represents the:

A.  value of y when x = 0.

B.  average change in y per unit change in x.

C.  value of x when y = 0.

D.  average change in x per unit change in y.

Analysis:

A. Incorrect. In the simple linear regression model, the slope represents the average change in y per unit change in x.

B. Correct. In the simple linear regression model, the slope represents the average change in y per unit change in x.

C. Incorrect. In the simple linear regression model, the slope represents the average change in y per unit change in x.

D. Incorrect. In the simple linear regression model, the slope represents the average change in y per unit change in x.

ANSWER: B Ref: Section 16.1-16.2

  1. Which of the following techniques is used to predict the value of one variable on the basis of other variables?
  1. Correlation analysis
  2. Coefficient of correlation
  3. Covariance
  4. Regression analysis

Analysis:

A. Incorrect. Regression analysis is used to predict the value.

B. Incorrect. Regression analysis is used to predict the value.

C. Incorrect. Regression analysis is used to predict the value.

D. Correct. Regression analysis is used to predict the value.

ANSWER: D Ref: Section 16.1-16.2

  1. The residual is defined as the difference between:

A.  the actual value of y and the estimated value of y

B.  the actual value of x and the estimated value of x

C.  the actual value of y and the estimated value of x

D.  the actual value of x and the estimated value of y

Analysis:

A. Correct. The residual is defined as the difference between the actual value of y and the estimated value of y

B. Incorrect. The residual is defined as the difference between the actual value of y and the estimated value of y

C. Incorrect. The residual is defined as the difference between the actual value of y and the estimated value of y

D. Incorrect. The residual is defined as the difference between the actual value of y and the estimated value of y

ANSWER: A Ref: Section 16.1-16.2

  1. In the simple linear regression model, the y-intercept represents the:

A.  change in y per unit change in x.

B.  change in x per unit change in y.

C.  value of y when x = 0.

D.  value of x when y = 0.

Analysis:

A. Incorrect. In the simple linear regression model, the y-intercept represents the value of y

when x = 0

B. Incorrect. In the simple linear regression model, the y-intercept represents the value of y

when x = 0

C. Correct. In the simple linear regression model, the y-intercept represents the value of y

when x = 0

D. Incorrect. In the simple linear regression model, the y-intercept represents the value of y

when x = 0

ANSWER: C Ref: Section 16.1-16.2

  1. In the first order linear regression model, the population parameters of the y-intercept and the slope are estimated respectively, by:
  1. and
  2. and
  3. and
  4. and

Analysis:

A. Correct. The y-intercept and the slope are estimated by and

B. Incorrect. The y-intercept and the slope are estimated by and

C. Incorrect. The y-intercept and the slope are estimated by and

D. Incorrect. The y-intercept and the slope are estimated by and

ANSWER: A Ref: Section 16.1-16.2

  1. The least squares method for determining the best fit minimizes the:
  1. total variation in the dependent variable.
  2. sum of squares for error.
  3. sum of squares for regression.
  4. All of these choices are true.

Analysis:

A. Incorrect. The least squares method for determining the best fit minimizes the sum of squares for error.

B. Correct. The least squares method for determining the best fit minimizes the sum of squares for error.

C. Incorrect. The least squares method for determining the best fit minimizes the sum of squares for error.

D. Incorrect. The least squares method for determining the best fit minimizes the sum of squares for error.

ANSWER: B Ref: Section 16.1-16.2

  1. In regression analysis, the residuals represent the:
  1. difference between the actual y values and their predicted values.
  2. difference between the actual x values and their predicted values.
  3. square root of the slope of the regression line.
  4. change in y per unit change in x.

Analysis:

A. Correct. In regression analysis, the residuals represent the difference between the actual y values and their predicted values.

B. Incorrect. In regression analysis, the residuals represent the difference between the actual y values and their predicted values.

C. Incorrect. In regression analysis, the residuals represent the difference between the actual y values and their predicted values.

D. Incorrect. In regression analysis, the residuals represent the difference between the actual y values and their predicted values.

ANSWER: A Ref: Section 16.1-16.2

  1. In simple linear regression, most often we perform a two-tail test of the population slope to determine whether there is sufficient evidence to infer that a linear relationship exists. The null hypothesis is stated as:
  4. None of these choices.

Analysis:

A. Correct. The null hypothesis is stated as

B. Incorrect. The null hypothesis is stated as

C. Incorrect. The null hypothesis is stated as

D. Incorrect. The null hypothesis is stated as

ANSWER: A Ref: Section 16.3-16.4

  1. Testing whether the slope of the population regression line could be zero is equivalent to testing whether the:
  1. sample coefficient of correlation could be zero.
  2. standard error of estimate could be zero.
  3. population coefficient of correlation could be zero.
  4. sum of squares for error could be zero.

Analysis:

A. Incorrect. It is equivalent to testing whether the population coefficient of correlation could be zero.

B. Incorrect. It is equivalent to testing whether the population coefficient of correlation could be zero.

C. Correct. It is equivalent to testing whether the population coefficient of correlation could be zero.

D. Incorrect. It is equivalent to testing whether the population coefficient of correlation could be zero.

ANSWER: C Ref: Section 16.3-16.4

  1. The symbol for the population coefficient of correlation is:
  1. r
  3. r

Analysis:

A. Incorrect. The symbol for the population coefficient of correlation is

B. Correct. The symbol for the population coefficient of correlation is

C. Incorrect. The symbol for the population coefficient of correlation is

D. Incorrect. The symbol for the population coefficient of correlation is

ANSWER: B Ref: Section 16.3-16.4

  1. The symbol for the sample coefficient of correlation is:

A.  r

Analysis:

A. Correct. The symbol for the sample coefficient of correlation is r

B. Incorrect. The symbol for the sample coefficient of correlation is r

C. Incorrect. The symbol for the sample coefficient of correlation is r

D. Incorrect. The symbol for the sample coefficient of correlation is r

ANSWER: A Ref: Section 16.3-16.4

  1. The coefficient of correlation is used to determine:
  1. the strength and direction of the linear relationship between x and y.
  2. the least squares estimates of the regression parameters.
  3. the predicted value of y for a given value of x.
  4. All of these choices.

Analysis:

A. Correct. The coefficient of correlation is used to determine the strength and direction of the linear relationship between x and y.

B. Incorrect. The coefficient of correlation is used to determine the strength and direction of the linear relationship between x and y.

C. Incorrect. The coefficient of correlation is used to determine the strength and direction of the linear relationship between x and y.

D. Incorrect. The coefficient of correlation is used to determine the strength and direction of the linear relationship between x and y.

ANSWER: A Ref: Section 16.3-16.4

  1. If the coefficient of correlation between x and y is close to 1.0, this indicates that:
  1. y causes x to happen.
  2. x causes y to happen.
  3. both (a) and (b) .
  4. there may or may not be a causal relationship between x and y.

Analysis:

A. Incorrect. If the coefficient of correlation between x and y is close to 1.0, this indicates that there may or may not be a causal relationship between x and y.

B. Incorrect. If the coefficient of correlation between x and y is close to 1.0, this indicates that there may or may not be a causal relationship between x and y.

C. Incorrect. If the coefficient of correlation between x and y is close to 1.0, this indicates that there may or may not be a causal relationship between x and y.

D. Correct. If the coefficient of correlation between x and y is close to 1.0, this indicates that there may or may not be a causal relationship between x and y.

ANSWER: X Ref: Section 16.3-16.4

  1. The confidence interval estimate of the expected value of y for a given value x, compared to the prediction interval of y for the same given value of x and confidence level, will be:
  1. wider.
  2. narrower.
  3. the same.
  4. impossible to know.

Analysis:

A. Incorrect. The confidence interval estimate will be narrower.

B. Correct. The confidence interval estimate will be narrower.

C. Incorrect. The confidence interval estimate will be narrower.

D. Incorrect. The confidence interval estimate will be narrower.

ANSWER: B Ref: Section 16.5

  1. The width of the confidence interval estimate for the predicted value of y depends on
  1. the standard error of the estimate
  2. the value of x for which the prediction is being made
  3. the sample size
  4. All of these choices are true.

Analysis:

A. Incorrect. All of these choices are true.

B. Incorrect. All of these choices are true.

C. Incorrect. All of these choices are true.

D. Correct. All of these choices are true.

ANSWER: D Ref: Section 16.5